Long Memory Volatility and Bernoulli Jumps in Daily Crypto Currency Prices

This paper investigates the intrinsic time series properties of daily crypto currency prices, the long memory volatility and the jumps. For the purpose, this paper first adopts the simple FIGARCH model to analyze the long memory volatility process of the crypto currency prices and finds that there exists the long memory volatility in the daily returns. But, the jumps are found to be significant in the daily returns so that the simple FIGARCH model appears to be inadequate. Thus, this paper uses a normal mixture distribution which includes the Bernoulli jumps in the daily returns. In particular, the jumps appear to make the long memory volatility more significant in the daily returns. The results imply that using simple FIGARCH model without the jumps may yield the incorrect long memory volatility process of the crypto currencies and result in ineffective risk management and portfolio optimization in the markets. Thus, the FIGARCH model with allowing for the jump process could be more appropriate in the aspects of risk management and investment purpose forecasting the risk in such an investment as this market attracts increasing attractions from regulators and investors.